Do I need the approval of my previous employer after resignation to move to another job?

I've resigned from my job during my probation and I've given my company a 15 days notice based on the following clause:

"This contract may be terminated prior to the expiry of the Probation, by either Party on 14 (minimum 14 calendar days’ notice) and without reason. Should the Employee wish to serve notice to terminate the Contract during the Probation in order to join another company in the UAE, the Employee will give the Employer at least a 30 calendar days written notice. The Employee shall not be entitled to any end-of-service gratuity payment if termination takes place during Probation."

My company approved and we've signed a settlement with neither party owing anything to the other and my visa has been canceled.

I still haven't taken on a job, but I wanted to know that should I take a job after this, and during my grace period, is it a must that I contact my previous employer.

Seeing as I would very much not want to involve my previous employer with these details.